sklearn.linear_model
.LassoLars¶
- class sklearn.linear_model.LassoLars(alpha=1.0, *, fit_intercept=True, verbose=False, normalize='deprecated', precompute='auto', max_iter=500, eps=2.220446049250313e-16, copy_X=True, fit_path=True, positive=False, jitter=None, random_state=None)[source]¶
Lasso model fit with Least Angle Regression a.k.a. Lars
It is a Linear Model trained with an L1 prior as regularizer.
The optimization objective for Lasso is:
(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1
Read more in the User Guide.
- Parameters
- alphafloat, default=1.0
Constant that multiplies the penalty term. Defaults to 1.0.
alpha = 0
is equivalent to an ordinary least square, solved byLinearRegression
. For numerical reasons, usingalpha = 0
with the LassoLars object is not advised and you should prefer the LinearRegression object.- fit_interceptbool, default=True
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be centered).
- verbosebool or int, default=False
Sets the verbosity amount.
- normalizebool, default=True
This parameter is ignored when
fit_intercept
is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please useStandardScaler
before callingfit
on an estimator withnormalize=False
.Deprecated since version 1.0:
normalize
was deprecated in version 1.0. It will default to False in 1.2 and be removed in 1.4.- precomputebool, ‘auto’ or array-like, default=’auto’
Whether to use a precomputed Gram matrix to speed up calculations. If set to
'auto'
let us decide. The Gram matrix can also be passed as argument.- max_iterint, default=500
Maximum number of iterations to perform.
- epsfloat, default=np.finfo(float).eps
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the
tol
parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.- copy_Xbool, default=True
If True, X will be copied; else, it may be overwritten.
- fit_pathbool, default=True
If
True
the full path is stored in thecoef_path_
attribute. If you compute the solution for a large problem or many targets, settingfit_path
toFalse
will lead to a speedup, especially with a small alpha.- positivebool, default=False
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients will not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (
alphas_[alphas_ > 0.].min()
when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator.- jitterfloat, default=None
Upper bound on a uniform noise parameter to be added to the
y
values, to satisfy the model’s assumption of one-at-a-time computations. Might help with stability.New in version 0.23.
- random_stateint, RandomState instance or None, default=None
Determines random number generation for jittering. Pass an int for reproducible output across multiple function calls. See Glossary. Ignored if
jitter
is None.New in version 0.23.
- Attributes
- alphas_array-like of shape (n_alphas + 1,) or list of such arrays
Maximum of covariances (in absolute value) at each iteration.
n_alphas
is eithermax_iter
,n_features
or the number of nodes in the path withalpha >= alpha_min
, whichever is smaller. If this is a list of array-like, the length of the outer list isn_targets
.- active_list of length n_alphas or list of such lists
Indices of active variables at the end of the path. If this is a list of list, the length of the outer list is
n_targets
.- coef_path_array-like of shape (n_features, n_alphas + 1) or list of such arrays
If a list is passed it’s expected to be one of n_targets such arrays. The varying values of the coefficients along the path. It is not present if the
fit_path
parameter isFalse
. If this is a list of array-like, the length of the outer list isn_targets
.- coef_array-like of shape (n_features,) or (n_targets, n_features)
Parameter vector (w in the formulation formula).
- intercept_float or array-like of shape (n_targets,)
Independent term in decision function.
- n_iter_array-like or int
The number of iterations taken by lars_path to find the grid of alphas for each target.
- n_features_in_int
Number of features seen during fit.
New in version 0.24.
See also
Examples
>>> from sklearn import linear_model >>> reg = linear_model.LassoLars(alpha=0.01, normalize=False) >>> reg.fit([[-1, 1], [0, 0], [1, 1]], [-1, 0, -1]) LassoLars(alpha=0.01, normalize=False) >>> print(reg.coef_) [ 0. -0.955...]
Methods
fit
(X, y[, Xy])Fit the model using X, y as training data.
get_params
([deep])Get parameters for this estimator.
predict
(X)Predict using the linear model.
score
(X, y[, sample_weight])Return the coefficient of determination \(R^2\) of the prediction.
set_params
(**params)Set the parameters of this estimator.
- fit(X, y, Xy=None)[source]¶
Fit the model using X, y as training data.
- Parameters
- Xarray-like of shape (n_samples, n_features)
Training data.
- yarray-like of shape (n_samples,) or (n_samples, n_targets)
Target values.
- Xyarray-like of shape (n_samples,) or (n_samples, n_targets), default=None
Xy = np.dot(X.T, y) that can be precomputed. It is useful only when the Gram matrix is precomputed.
- Returns
- selfobject
returns an instance of self.
- get_params(deep=True)[source]¶
Get parameters for this estimator.
- Parameters
- deepbool, default=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
- Returns
- paramsdict
Parameter names mapped to their values.
- predict(X)[source]¶
Predict using the linear model.
- Parameters
- Xarray-like or sparse matrix, shape (n_samples, n_features)
Samples.
- Returns
- Carray, shape (n_samples,)
Returns predicted values.
- score(X, y, sample_weight=None)[source]¶
Return the coefficient of determination \(R^2\) of the prediction.
The coefficient \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares
((y_true - y_pred) ** 2).sum()
and \(v\) is the total sum of squares((y_true - y_true.mean()) ** 2).sum()
. The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value ofy
, disregarding the input features, would get a \(R^2\) score of 0.0.- Parameters
- Xarray-like of shape (n_samples, n_features)
Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape
(n_samples, n_samples_fitted)
, wheren_samples_fitted
is the number of samples used in the fitting for the estimator.- yarray-like of shape (n_samples,) or (n_samples, n_outputs)
True values for
X
.- sample_weightarray-like of shape (n_samples,), default=None
Sample weights.
- Returns
- scorefloat
\(R^2\) of
self.predict(X)
wrt.y
.
Notes
The \(R^2\) score used when calling
score
on a regressor usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).
- set_params(**params)[source]¶
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as
Pipeline
). The latter have parameters of the form<component>__<parameter>
so that it’s possible to update each component of a nested object.- Parameters
- **paramsdict
Estimator parameters.
- Returns
- selfestimator instance
Estimator instance.